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学者姓名：徐茂智
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Abstract ：
求根问题是计算数论中的一个困难性问题,为了提高求根问题的求解效率和扩大量子计算的应用范围,对求根问题进行了量子算法的分析.在两大量子算法Shor算法和Grover算法的基础上,提出了2种解决求根问题的量子算法RF-Shor算法和RF-Grover算法.经分析,RF-Shor算法需要多项式规模的量子门资源,能以接近1的概率求出求根问题的所有解.在没有使用任何可提高搜索效率的经典策略的情况下,RF-Grover算法能在O(M/k)步内以至少1/2的概率求出求根问题k个解中的一个解.
Keyword ：
Shor算法 Shor算法 求根问题 求根问题 量子算法 量子算法 Grover算法 Grover算法
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| GB/T 7714 | 孙国栋 , 苏盛辉 , 徐茂智 . 求根问题的量子计算算法 [J]. | 北京工业大学学报 , 2015 , 41 (03) : 366-371 . |
| MLA | 孙国栋 等. "求根问题的量子计算算法" . | 北京工业大学学报 41 . 03 (2015) : 366-371 . |
| APA | 孙国栋 , 苏盛辉 , 徐茂智 . 求根问题的量子计算算法 . | 北京工业大学学报 , 2015 , 41 (03) , 366-371 . |
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Abstract ：
The authors give the definition and property of a bit-pair shadow, and design the algorithms of a public key cryptoscheme based on a multivariate permutation problem and an anomalous subset product problem to which no subexponential time solutions are found so far, and regards a bit-pair as an operation unit. Further, demonstrate that the decryption algorithm is correct, deduce the probability that a plaintext solution is nonunique is nearly zero, analyze the security of the new scheme against extracting a private key from a public key and recovering a plaintext from a ciphertext on the assumption that an integer factorization problem, a discrete logarithm problem, and a low-density subset sum problem can be solved efficiently, and prove that new scheme using random padding and permutation is semantically secure. The analysis shows that the bit-pair method increases the density D of a related knapsack to 1+, and decreases the modulus length inverted right perpendicular lg M inverted left perpendicular of the new scheme to 464, 544, or 640.
Keyword ：
Anomalous subset sum problem Anomalous subset sum problem Bit-pair shadow Bit-pair shadow Compact sequence Compact sequence Public key cryptoscheme Public key cryptoscheme Random padding Random padding Semantical security Semantical security
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| GB/T 7714 | Su, Shenghui , Lu, Shuwang , Xu, Maozhi . A Public Key Cryptoscheme Using Bit-Pairs with Provable Semantical Security [C] . 2015 : 674-686 . |
| MLA | Su, Shenghui 等. "A Public Key Cryptoscheme Using Bit-Pairs with Provable Semantical Security" . (2015) : 674-686 . |
| APA | Su, Shenghui , Lu, Shuwang , Xu, Maozhi . A Public Key Cryptoscheme Using Bit-Pairs with Provable Semantical Security . (2015) : 674-686 . |
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Abstract ：
Quantum computation is a new computing model based on fundamental quantum mechanical principle. Grover's algorithm finds the solution for a searching problem in the square root time of exhaustive search. Brassard, Hoyer, Tapp's algorithm counts the number of solutions for a searching problem. Through exploiting the two quantum algorithms, we propose a quantum algorithm for solving a new cryptography problem----polynomial root finding problem, which could be used to design a cryptosystem. The algorithm will take O(root M/t) steps for finding one of the t solutions to the problem, where M is the modular of the equation. The success rate of the algorithm is a constant and the cost of the algorithm depends on the calculations of modular exponentiation and the number of iterations.
Keyword ：
Polynomial root finding problem Polynomial root finding problem Quantum counting Quantum counting Quantum searching Quantum searching Signature algorithm Signature algorithm
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| GB/T 7714 | Sun, Guodong , Su, Shenghui , Xu, Maozhi . Quantum Algorithm for Polynomial Root Finding Problem [C] . 2014 : 469-473 . |
| MLA | Sun, Guodong 等. "Quantum Algorithm for Polynomial Root Finding Problem" . (2014) : 469-473 . |
| APA | Sun, Guodong , Su, Shenghui , Xu, Maozhi . Quantum Algorithm for Polynomial Root Finding Problem . (2014) : 469-473 . |
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Abstract ：
Quantum computation is a new computational model based on quantum mechanical principle. Shor invented the polynomial time algorithms for the prime factorization and discrete logarithm problem, which indicated that the cryptosystems based on them are totally unsafe in the quantum world. Grover constructed an algorithm that finds a solution in only O(√2 n )steps whereas the exhaustive search algorithm needs O(2 n ) steps on average. In this paper we investigate the cryptanalysis of a new cryptography problem-multivariate permutation problem (MPP), which could be used to design public-key cryptosystem, with the help of the two quantum algorithms. Specially, we discuss the strength of a private key of the REESSE1+ public-key cryptosystem, whose security is based on the hardness of MPP. Besides, some suggestions are also given about the implementation of the REESSE1+.
Keyword ：
Public key cryptography Public key cryptography Polynomial approximation Polynomial approximation Quantum computers Quantum computers Algorithms Algorithms Quantum cryptography Quantum cryptography Factorization Factorization Quantum theory Quantum theory
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| GB/T 7714 | Sun, Guodong , Su, Shenghui , Xu, Maozhi . Quantum cryptanalysis of multivariate permutation problem [J]. | International Journal of Security and its Applications , 2014 , 8 (6) : 261-272 . |
| MLA | Sun, Guodong 等. "Quantum cryptanalysis of multivariate permutation problem" . | International Journal of Security and its Applications 8 . 6 (2014) : 261-272 . |
| APA | Sun, Guodong , Su, Shenghui , Xu, Maozhi . Quantum cryptanalysis of multivariate permutation problem . | International Journal of Security and its Applications , 2014 , 8 (6) , 261-272 . |
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